Closed-loop Control of DC Drives with Controlled Rectifier

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• Closed-loop Control of DC Drives with Controlled
  Rectifier
• By
• Mr.M.Kaliamoorthy
• Department of Electrical Electronics
  Engineering
• PSNA College of Engineering and Technology

2
Outline

• Closed Loop Control of DC Drives
• Closed-loop Control with Controlled Rectifier
• Two-quadrant
• Transfer Functions of Subsystems
• Design of Controllers
• Closed-loop Control with Field Weakening
• Two-quadrant
• Closed-loop Control with Controlled Rectifier
• Four-quadrant
• References

3
Closed Loop Control of DC Drives

• Closed loop control is when the firing angle is
  varied automatically by a controller to achieve a
  reference speed or torque
• This requires the use of sensors to feed back the
  actual motor speed and torque to be compared with
  the reference values

Output signal
Referencesignal
Plant
Controller

?
Sensor
4
Closed Loop Control of DC Drives

• Feedback loops may be provided to satisfy one or
  more of the following
• Protection
• Enhancement of response fast response with
  small overshoot
• Improve steady-state accuracy
• Variables to be controlled in drives
• Torque achieved by controlling current
• Speed
• Position

5
Closed Loop Control of DC Drives

• Cascade control structure
• Flexible outer loops can be added/removed
  depending on control requirements.
• Control variable of inner loop (eg speed,
  torque) can be limited by limiting its reference
  value
• Torque loop is fastest, speed loop slower and
  position loop - slowest

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Closed Loop Control of DC Drives

• Cascade control structure
• Inner Torque (Current) Control Loop
• Current control loop is used to control torque
  via armature current (ia) and maintains current
  within a safe limit
• Accelerates and decelerates the drive at maximum
  permissible current and torque during transient
  operations

Torque (Current) Control Loop
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Closed Loop Control of DC Drives

• Cascade control structure
• Speed Control Loop
• Ensures that the actual speed is always equal to
  reference speed ?
• Provides fast response to changes in ?, TL and
  supply voltage (i.e. any transients are overcome
  within the shortest feasible time) without
  exceeding motor and converter capability

Speed Control Loop
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Closed Loop Control with Controlled Rectifiers
Two-quadrant
Current Control Loop

• Two-quadrant Three-phase Controlled Rectifier DC
  Motor Drives

Speed Control Loop
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Closed Loop Control with Controlled Rectifiers
Two-quadrant

• Actual motor speed ?m measured using the
  tachogenerator (Tach) is filtered to produce
  feedback signal ?mr
• The reference speed ?r is compared to ?mr to
  obtain a speed error signal
• The speed (PI) controller processes the speed
  error and produces the torque command Te
• Te is limited by the limiter to keep within the
  safe current limits and the armature current
  command ia is produced
• ia is compared to actual current ia to obtain a
  current error signal
• The current (PI) controller processes the error
  to alter the control signal vc
• vc modifies the firing angle ? to be sent to the
  converter to obtained the motor armature voltage
  for the desired motor operation speed

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Closed Loop Control with Controlled Rectifiers
Two-quadrant

• Design of speed and current controller (gain and
  time constants) is crucial in meeting the dynamic
  specifications of the drive system
• Controller design procedure
• Obtain the transfer function of all drive
  subsystems
• DC Motor Load
• Current feedback loop sensor
• Speed feedback loop sensor
• Design current (torque) control loop first
• Then design the speed control loop

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Transfer Function of Subsystems DC Motor and
Load

• Assume load is proportional to speed
• DC motor has inner loop due to induced emf
  magnetic coupling, which is not physically seen
• This creates complexity in current control loop
  design

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Transfer Function of Subsystems DC Motor and
Load

• Need to split the DC motor transfer function
  between ?m and Va
• (1)
• where
• (2)
• (3)
• This is achieved through redrawing of the DC
  motor and load block diagram.

Back
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Transfer Function of Subsystems DC Motor and
Load

• In (2),
• - mechanical motor time constant (4)
• - motor and load friction coefficient (5)
• In (3),
• (6)
• (7)
• Note J motor inertia, B1 motor friction
  coefficient, BL load friction coefficient

Back
14
Transfer Function of Subsystems Three-phase
Converter

• Need to obtain linear relationship between
  control signal vc and delay angle ? (i.e. using
  cosine wave crossing method)
• (8)
• where vc control signal (output of current
  controller)
• Vcm maximum value of the
  control voltage
• Thus, dc output voltage of the three-phase
  converter
• (9)

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Transfer Function of Subsystems Three-phase
Converter

• Gain of the converter
• (10)
• where V rms line-to-line voltage of
  3-phase supply
• Converter also has a delay
• (11)
• where fs supply voltage frequency
• Hence, the converter transfer function
• (12)

Back
16
Transfer Function of Subsystems Current and
Speed Feedback

• Current Feedback
• Transfer function
• No filtering is required in most cases
• If filtering is required, a low pass-filter can
  be included (time constant lt 1ms).
• Speed Feedback
• Transfer function
• (13)
• where K? gain, T? time constant
• Most high performance systems use dc tacho
  generator and low-pass filter
• Filter time constant lt 10 ms

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Design of Controllers Block Diagram of Motor
Drive
Current Control Loop
Speed Control Loop

• Control loop design starts from inner (fastest)
  loop to outer(slowest) loop
• Only have to solve for one controller at a time
• Not all drive applications require speed control
  (outer loop)
• Performance of outer loop depends on inner loop

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Design of Controllers Current Controller
DC Motor Load
Controller
Converter

• PI type current controller
  (14)
• Open loop gain function
• (15)
• From the open loop gain, the system is of 4th
  order (due to 4 poles of system)

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Design of Controllers Current Controller

• If designing without computers, simplification
  is needed.
• Simplification 1 Tm is in order of 1 second.
  Hence,
• (16)
• Hence, the open loop gain function becomes
• i.e. system zero cancels the controller pole
  at origin.

(17)
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Design of Controllers Current Controller

• Relationship between the denominator time
  constants in (17)
• Simplification 2 Make controller time constant
  equal to T2
• (18)
• Hence, the open loop gain function becomes
• i.e. controller zero cancels one of the system
  poles.

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Design of Controllers Current Controller

• After simplification, the final open loop gain
  function
• (19)
• where
  (20)
• The system is now of 2nd order.
• From the closed loop transfer function
  ,
• the closed loop characteristic equation is
• or when expanded becomes
  (21)

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Design of Controllers Current Controller

• Design the controller by comparing system
  characteristic equation (eq. 21) with the
  standard 2nd order system equation
• Hence,
• So, for good dynamic performance ?0.707
• Hence equating the damping ratio to 0.707 in (23)
  we get

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Squaring the equation on both sides
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Which leads to
An approximation K gtgt 1
Equating above expression with (20) we get the
gain of current controller
Back
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Design of Controllers Current loop 1st order
approximation

• To design the speed loop, the 2nd order model of
  current loop must be replaced with an approximate
  1st order model
• Why?
• To reduce the order of the overall speed loop
  gain function

2nd order current loop model
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Design of Controllers Current loop 1st order
approximation

• Approximated by adding Tr to T1 ?
• Hence, current model transfer function is given
  by
• (24)

1st order approximation of current loop
Full derivation available here.
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Design of Controllers Current Controller

• After simplification, the final open loop gain
  function

• Where

• Since

• and since

• Therefore

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Design of Controllers Current loop 1st order
approximation

• where
  
  (26)
• (27)
• (28)
• 1st order approximation of current loop used in
  speed loop design.
• If more accurate speed controller design is
  required, values of Ki and Ti should be obtained
  experimentally.

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Design of Controllers Speed Controller
DC Motor Load

• PI type speed controller
  (29)
• Assume there is unity speed feedback
• (30)

1st order approximation of current loop
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Design of Controllers Speed Controller
DC Motor Load

• Open loop gain function
• (31)
• From the loop gain, the system is of 3rd order.
• If designing without computers, simplification
  is needed.

1st order approximation of current loop
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Design of Controllers Speed Controller

• Relationship between the denominator time
  constants in (31)
• (32)
• Hence, design the speed controller such that
• (33)
• The open loop gain function becomes
• i.e. controller zero cancels one of the system
  poles.

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Design of Controllers Speed Controller

• After simplification, loop gain function
• (34)
• where
  (35)
• The controller is now of 2nd order.
• From the closed loop transfer function
  ,
• the closed loop characteristic equation is
• or when expanded becomes (36)

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Design of Controllers Speed Controller

• Design the controller by comparing system
  characteristic equation with the standard
  equation
• Hence
• (37)
• (38)
• So, for a given value of ?
• use (37) to calculate ?n
• Then use (38) to calculate the controller gain KS
  

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Closed Loop Control with Field Weakening
Two-quadrant

• Motor operation above base speed requires field
  weakening
• Field weakening obtained by varying field winding
  voltage using controlled rectifier in
• single-phase or
• three-phase
• Field current has no ripple due to large Lf
• Converter time lag negligible compared to field
  time constant
• Consists of two additional control loops on field
  circuit
• Field current control loop (inner)
• Induced emf control loop (outer)

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Closed Loop Control with Field Weakening
Two-quadrant
Field weakening
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Closed Loop Control with Field Weakening
Two-quadrant
Field weakening
Field current controller (PI-type)
Estimated machine -induced emf
Induced emf controller (PI-type with limiter)
Field current reference
Induced emf reference
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Closed Loop Control with Field Weakening
Two-quadrant

• The estimated machine-induced emf is obtained
  from
• (the estimated emf is machine-parameter
  sensitive and must be adaptive)
• The reference induced emf e is compared to e to
  obtain the induced emf error signal (for speed
  above base speed, e kept constant at rated emf
  value so that ? ? 1/?)
• The induced emf (PI) controller processes the
  error and produces the field current reference
  if
• if is limited by the limiter to keep within the
  safe field current limits
• if is compared to actual field current if to
  obtain a current error signal
• The field current (PI) controller processes the
  error to alter the control signal vcf (similar to
  armature current ia control loop)
• vcf modifies the firing angle ?f to be sent to
  the converter to obtained the motor field voltage
  for the desired motor field flux

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Closed Loop Control with Controlled Rectifiers
Four-quadrant

• Four-quadrant Three-phase Controlled Rectifier DC
  Motor Drives

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Closed Loop Control with Controlled Rectifiers
Four-quadrant

• Control very similar to the two-quadrant dc motor
  drive.
• Each converter must be energized depending on
  quadrant of operation
• Converter 1 for forward direction / rotation
• Converter 2 for reverse direction / rotation
• Changeover between Converters 1 2 handled by
  monitoring
• Speed
• Current-command
• Zero-crossing current signals
• Selector block determines which converter has
  to operate by assigning pulse-control signals
• Speed and current loops shared by both converters
• Converters switched only when current in outgoing
  converter is zero (i.e. does not allow
  circulating current. One converter is on at a
  time.)

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References

• Krishnan, R., Electric Motor Drives Modeling,
  Analysis and Control, Prentice-Hall, New Jersey,
  2001.
• Rashid, M.H, Power Electronics Circuit, Devices
  and Applictions, 3rd ed., Pearson, New-Jersey,
  2004.
• Nik Idris, N. R., Short Course Notes on
  Electrical Drives, UNITEN/UTM, 2008.

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DC Motor and Load Transfer Function - Decoupling
of Induced EMF Loop

• Step 1
• Step 2

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DC Motor and Load Transfer Function - Decoupling
of Induced EMF Loop

• Step 3
• Step 4

Back
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Cosine-wave Crossing Control for Controlled
Rectifiers
Vm
Input voltageto rectifier
Cosine wave compared with control voltage vc
Cosine voltage
Vcmcos(?) vc
Results of comparison trigger SCRs
Output voltageof rectifier
Back
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Design of Controllers Current loop 1st order
approximation
Back
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